This puzzle is based on the dissection of a square into four pieces which can be rearranged to form a triangle. Given the four pieces the problem is to assemble them into first a square tray and second into a triangular tray.
This is a revisit to the Haberdasher Puzzle: http://www.thingiverse.com/thing:1457184. It was redone to be uniform with puzzles described in thing:1481244 and thing:1492552. All the square boxes for these puzzles are the same size so that multiple puzzles can be combined to make the solutions more difficult.
A simple, elegant method, described by Harry Lindgren, was used to form the puzzle pieces. Lindgren showed how to get a solution to the Haberdasher's problem using images on tracing paper. Two sheets containing traces of adjacent polygons are formed; a strip of squares and a strip of triangles. The two sheets are then overlapped and the triangular strip rotated and shifted until a solution is found. An image of the two strips overlaid at the correct position is shown above. The solution appears in the square on the right. More details are provided in the openSCAD code.